A complete model of shear dispersion in pipes
 G. N. Mercer,
 A. J. Roberts
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High order models of the longitudinal dispersion of a passive contaminant in Poiseuille pipe flow are derive and their validity discussed. The derivation is done using centre manifold theory which provides a systematic and consistent approach to calculating each successive approximation. A stable, nonnegative finite difference scheme is formulated which matches the evolution equation to a predetermined order. The limitations imposed by this matching is investigated. The appropriate initial conditions to use for the Taylor model of shear dispersion in pipes are derived. It is shown that the commonly used initial condition of simply taking the crosssectional average is only a first approximation to the correct initial condition. In a similar manner the correct boundary conditions to be used at the inlet and outlet of a finite length pipe are derived. The generalisation to a pipe with varying crosssection and varying flow properties is studied and the resultant modifications to the advection velocity and the effective dispersion coefficient are calculated. An example of an exponentially varying pipe is considered and the differences between this approach and the classical Taylor theory are examined.
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 Title
 A complete model of shear dispersion in pipes
 Journal

Japan Journal of Industrial and Applied Mathematics
Volume 11, Issue 3 , pp 499521
 Cover Date
 19941001
 DOI
 10.1007/BF03167234
 Print ISSN
 09167005
 Online ISSN
 1868937X
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 shear dispersion
 centre manifold
 pipes
 Industry Sectors
 Authors

 G. N. Mercer ^{(1)}
 A. J. Roberts ^{(2)}
 Author Affiliations

 1. Mathematics Department, University College, Australian Defence Force Academy, University of New South Wales, 2600, Canberra, ACT, Australia
 2. Mathematics Department, University of Southern Queensland, 4350, Toowoomba, Queensland, Australia